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Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural…

Machine Learning · Statistics 2025-10-30 Andrea Montanari , Pierfrancesco Urbani

Deep double descent is one of the key phenomena underlying the generalization capability of deep learning models. In this study, epoch-wise double descent, which is delayed generalization following overfitting, was empirically investigated…

Machine Learning · Computer Science 2026-01-14 Tomoki Kubo , Ryuken Uda , Yusuke Iida

Finding the optimal size of deep learning models is very actual and of broad impact, especially in energy-saving schemes. Very recently, an unexpected phenomenon, the ``double descent'', has caught the attention of the deep learning…

Machine Learning · Computer Science 2023-12-27 Victor Quétu , Enzo Tartaglione

Unlike the conventional wisdom in statistical learning theory, the test error of a deep neural network (DNN) often demonstrates double descent: as the model complexity increases, it first follows a classical U-shaped curve and then shows a…

Machine Learning · Computer Science 2021-06-04 Xiao Zhang , Dongrui Wu , Haoyi Xiong , Bo Dai

We study the generalization behavior of transfer learning of deep neural networks (DNNs). We adopt the overparameterization perspective -- featuring interpolation of the training data (i.e., approximately zero train error) and the double…

Machine Learning · Computer Science 2023-06-13 Yehuda Dar , Lorenzo Luzi , Richard G. Baraniuk

It has been observed by Belkin et al.\ that over-parametrized neural networks exhibit a `double descent' phenomenon. That is, as the model complexity (as reflected in the number of features) increases, the test error initially decreases,…

Optimization and Control · Mathematics 2025-09-16 Vivek Shripad Borkar

`Double descent' delineates the generalization behaviour of models depending on the regime they belong to: under- or over-parameterized. The current theoretical understanding behind the occurrence of this phenomenon is primarily based on…

Machine Learning · Statistics 2022-03-15 Sidak Pal Singh , Aurelien Lucchi , Thomas Hofmann , Bernhard Schölkopf

Deep learning methods operate in regimes that defy the traditional statistical mindset. Neural network architectures often contain more parameters than training samples, and are so rich that they can interpolate the observed labels, even if…

Statistics Theory · Mathematics 2020-12-14 Song Mei , Andrea Montanari

Deep learning models, particularly Transformers, have achieved impressive results in various domains, including time series forecasting. While existing time series literature primarily focuses on model architecture modifications and data…

Machine Learning · Computer Science 2023-12-01 Valentino Assandri , Sam Heshmati , Burhaneddin Yaman , Anton Iakovlev , Ariel Emiliano Repetur

Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data. We study this phenomenon by analysing the dynamics and the performance of over-parameterised two-layer neural…

Machine Learning · Statistics 2022-03-28 Sebastian Goldt , Madhu S. Advani , Andrew M. Saxe , Florent Krzakala , Lenka Zdeborová

This paper investigates the double descent phenomenon in two-layer neural networks, focusing on the role of L1 regularization and representation dimensions. It explores an alternative double descent phenomenon, named sparse double descent.…

Machine Learning · Computer Science 2024-01-22 Ya Shi Zhang

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical…

Machine Learning · Computer Science 2024-01-24 Cheng Shi , Liming Pan , Hong Hu , Ivan Dokmanić

In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a…

Machine Learning · Computer Science 2022-06-08 Marco Loog , Tom Viering , Alexander Mey , Jesse H. Krijthe , David M. J. Tax

A recent line of research has highlighted the existence of a "double descent" phenomenon in deep learning, whereby increasing the number of training examples $N$ causes the generalization error of neural networks to peak when $N$ is of the…

Machine Learning · Computer Science 2022-01-12 Stéphane d'Ascoli , Levent Sagun , Giulio Biroli

Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…

Machine Learning · Computer Science 2020-05-26 Wesley J. Maddox , Gregory Benton , Andrew Gordon Wilson

We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visualizations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes…

Optimization plays a key role in the training of deep neural networks. Deciding when to stop training can have a substantial impact on the performance of the network during inference. Under certain conditions, the generalization error can…

Machine Learning · Computer Science 2021-09-20 Florian Dubost , Erin Hong , Max Pike , Siddharth Sharma , Siyi Tang , Nandita Bhaskhar , Christopher Lee-Messer , Daniel Rubin

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…

Machine Learning · Computer Science 2020-05-04 Melikasadat Emami , Mojtaba Sahraee-Ardakan , Parthe Pandit , Sundeep Rangan , Alyson K. Fletcher

The dynamics of gradient-based training in neural networks often exhibit nontrivial structures; hence, understanding them remains a central challenge in theoretical machine learning. In particular, a concept of feature unlearning, in which…

Machine Learning · Computer Science 2026-02-10 Shota Imai , Sota Nishiyama , Masaaki Imaizumi

Double descent presents a counter-intuitive aspect within the machine learning domain, and researchers have observed its manifestation in various models and tasks. While some theoretical explanations have been proposed for this phenomenon…

Machine Learning · Computer Science 2024-05-14 Yufei Gu